Americans overwhelmingly support tougher background checks for prospective gun owners, and a majority support bans on assault weapons and big ammunition clips, according to a new McClatchy-Marist poll.

The poll found that by a lopsided 84 to 15 percent, voters want background checks for private gun sales and sales at gun shows, with broad support from Democrats, independents and Republicans alike.

By 56-41 percent, they want a ban on assault weapons, and they support a ban on ammunition clips that hold more than 10 bullets by 52-45 percent, the survey found.

The poll results came as the Senate Judiciary Committee started considering those and other measures. The committee began voting on gun control measures last week , and it voted largely along party lines – Democrats for and Republicans against – for the first measure, banning “straw” purchases, in which people buy guns for people who are barred from doing so. Votes on other measures, including an assault weapons ban, are expected this week.

Despite majority support for some specific proposals, Americans remain split when they’re given a choice between protecting gun rights or curbing gun violence.

“The renewed debate on guns certainly hasn’t fostered any consensus,” said Lee Miringoff, the director of the Marist Institute for Public Opinion in New York, which conducted the poll March 4-7.

The survey also found that Americans have widely differing views on how to proceed on immigration, another issue that’s high on the Obama administration’s priority list.

Guns and immigration are expected to provide some of this year’s most heated congressional debate. Since a gunman killed 20 children and six adults Dec. 14 at Connecticut’s Sandy Hook Elementary School, President Barack Obama and many congressional Democrats have launched a push for stronger gun-control laws. They’ve run into resistance from gun owners, as well as Democrats and Republicans from states where gun rights are popular.

The poll reflects that split. Among registered voters, 49 percent thought protecting gun rights was important, while an equal percentage said the same about controlling gun violence

More than three of four Democrats wanted steps to curb gun violence. Nearly the same proportion of Republicans cited gun rights as more significant.

Support for gun rights was strongest in the South, where 53 percent labeled it a priority, and weakest in the Northeast, where the idea got 39 percent backing. Conversely, gun control was most popular in the Northeast and least popular in the South.

There was a strong consensus against diluting regulations on gun purchases to make it easier to buy and own guns. But the unity evaporated when the question involved assault weapons, which 55 percent want banned, and ammunition clips holding more than 10 bullets, which slightly more than half want barred.

Immigration issues have found more bipartisan cooperation in Washington as the White House and congressional Republicans try to find solutions, but the Marist data didn’t reflect much consensus.

Thirty-seven percent said immigration policy should be an immediate priority, but 46 percent thought it should be a priority only over the next few years. Nearly half of Republicans wanted quick action, while half the Democrats thought an overhaul could wait.

The thorniest piece of this puzzle involves whether to create a path to citizenship for people who entered the country illegally, but the poll found little enthusiasm. Forty-one percent said policy changes should mostly be about finding that path, while 55 percent would rather see changes in protecting the borders.